There　always　exist　approximation　errors　during　neural　network　control　processes,　which　may　cause　the　estimation　value　to　exceed　the　control　constraint　when　the　optimal　control　input　reaches　to　a　neighborhood　of　the　constraint.　In　this　paper,　through　a　new　neural　network　training　approach,　the　near-optimal　control　problem　for　a　class　of　nonlinear　discrete-time　systems　with　control　constraints　is　solved.　Based　on　the　nonquadratic　performance　index　and　the　dual　heuristic　dynamic　programming　scheme,　the　iterative　algorithm　is　developed　with　convergence　guarantee　and　is　also　implemented　by　using　three　neural　networks.　At　last,　two　examples　are　given　to　demonstrate　the　effectiveness　of　the　proposed　optimal　control　scheme.　©　2020　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.